Singularities in the Midwest, III.
Schedule of Talks
All talks will be in room B239 in Van Vleck Hall.
Coffee breaks and discussions will be in the 9th floor lounge, Room 911, in Van Vleck Hall.

March 21 
March 22 
March 23 
March 24 
99:50 




10:0010:30 
Coffee Break 
Coffee Break 
Coffee Break 
Coffee Break 
10:3011:20 




11:3012:20 




LUNCH 
Lunch 
Lunch 
Lunch 
Lunch 
15:0015:50 




16:0016:50 




Titles and Abstracts
 Sylvain Cappell:
Geometrical Combinatorics of Subcomplexes using Torsion Numbers
We report some ongoing progress on formulae which count geometrical subcomplexes,
satisfying varied conditions, of general complexes. Some of the results are new even for graphs and subgraphs,
generalizing the classical results of Kirchhoff and of Trent. For highdimensional complexes the general
formulae obtained are yielding
homological interpretations to the positive integer weights which arise. This is joint work with Edward Miller.
 José Ignacio Cogolludo Agustín:
 Manuel González Villa:
Recursions for motivic iterated vanishing cycles of quasiordinary surface singularities
We report on a project to apply formulas for the motivic iterated vanishing cycles,
introduced by Guibert, Loeser and Merle, to the case of quasiordinary surface singularities.
We aim to describe recursive relations between the invariant of the original quasiordinary
singularity and those of other two related singularities (a truncation and a derived object).
(This is joint work with Mirel Caibar, Gary Kennedy and Lee McEwan.)
 Eugene Gorsky:
Algebraic links and Heegaard Floer homology
Campillo, Delgado and GuseinZade related the coefficients of the Alexander polynomial of an algebraic link to
the Euler characteristics of some strata in the space of functions on the corresponding plane curve singularity.
I will explain the relation between the homology of these strata and link Floer homology. As a consequence,
I will describe a surprising combinatorial question about twocomponent links, motivated by the subtle topological
properties of Dehn surgeries along them. This is a joint work with Andras Nemethi.
 Denis Ibadula:
The real poles of the Igusa zeta function for curves
The candidate poles of the Igusa's padic zeta function are determined by the numerical data of
an embedded resolution. Using certain relations between these numerical data, we determine in complete
generality which real candidate poles are actual poles and which of them cancel out in the curve case.
(Joint work with Dirk Segers, Katholieke University of Leuven, Belgium.)
 Anatoly Libgober:
Strata of Discriminantal arrangements
In 1987 ManinSchechtman proposed
a generalization of braid arrangements such that
the fundamental groups of the complements
to these discriminantal arrangements provide
a natural generalizations of pure braid groups.
It turns out that such fundamental groups
depend on "hidden" parameters controlling the
structure of codimension 2 strata of ManinSchechtman
arrangements. We shall describe these possible
variations in the structure of codimension 2 strata
of discriminantal arrangements and
respective variations in the fundamental groups.
(This is report on join work with Simona Settepanella).
 Yongqiang Liu:
Alexander modules on hypersurface complement and its boundary manifold
We give a polynomial identity involving local and global Alexander polynomials,
generalizing a similar formula proved by Cogolludo and Florens in the case of plane curves.
The error terms in this identity can be further refined by using Reidemeister torsion.
If time allows, we will also show how to construct mixed Hodge structures on the
Alexander modules of the boundary manifold.
This is a joint work with Laurentiu Maxim.
 Ignacio Luengo:
Yano's conjecture for 2Puiseux pair curve singularities
In 1982, Yano proposed a conjecture predicting the bexponents of an irreducible plane
curve singularity which is generic in its equisingularity class. In this article we prove
the conjecture for the case of two Puiseux pairs and monodromy with distinct eigenvalues.
The hypothesis on the monodromy implies that the bexponents coincide with the opposite of
the roots of the Bernstein polynomial, and we compute the roots of the Bernstein polynomial.
 Lee McEwan:
Topology of the Milnor Fiber for a QuasiOrdinary Hypersurface
Let X = {f = 0} be the germ of a quasiordinary hypersurface, M = {f = ε} its Milnor fiber,
and ∂M the boundary of M. In the surface case, ∂M can be constructed in terms of the
vertical monodromy actions on slices of M, corresponding to points on a circle within each component of
X_{sing}. We give the Betti numbers of ∂M in terms of a recursive formula involving only the
characteristic tuples of f. This is applied to calculate the Betti numbers of M itself.
We also write down a conjectural formula for the monodromy of M.
Lastly we describe the likely extension of these results to dimension n, and some conjectures about the discriminate of M.
 Alejandro Melle Hernández:
On some conjectures about irreducible free and nearly free divisors
In this talk some examples of irreducible free and nearly
free curves in the complex projective plane which are not rational curves and
whose local singularites can have an arbitrary number of branches are given.
All these examples answer negatively to some conjectures proposed by A. Dimca
and G. Sticlaru. Our examples say nothing about the most remarkable conjecture
by A. Dimca and G. Sticlaru: every rational cuspidal plane curve is either
free or nearly free. This is a joint work with E. Artal, L. Gorrochategui and I. Luengo.
 Jörg Schürmann:
Cohomology representations of external and symmetric products of varieties
We explain refined generating series formulae for characters of (virtual) cohomology representations
of external products of suitable coefficients on (possibly singular) complex quasiprojective varieties,
e.g., (complexes of) constructible or coherent sheaves, or (complexes of) mixed Hodge modules.
These formulae generalize our previous results for symmetric and alternating powers of such coefficients,
and apply also to other Schur functors. The proofs of these results are reduced via an equivariant Kuenneth
formula to a more general generating series identity for abstract characters of tensor powers V^{⊗n} of an
element V in a suitable symmetric monoidal category.
This abstract approach applies directly also in the equivariant context for varieties with
additional symmetries (e.g., finite group actions, finite order automorphisms, resp., endomorphisms). This is joint work with
Laurentiu Maxim (see arXiv:1602.06546).
 Julius Shaneson:
Topological String Junctions, Gauge Groups, Outer Monodromy, and Matter
In string theory, the existence of "matter" comes via complex codimension two singularities of elliptic fibrations.
We discuss how to identify the gauge algebras and matter representations using deformations, rather than resolutions,
by means of a calculation of outer monodromy operators. This approach permits the analysis of various new cases
including some where an appropriate (crepant) resolutions may not even be available.
Some of these cases will be discussed. Possible progress towards a more totally topological theory,
if there is enough time (and progress), may also be mentioned.
The material comes from various joint projects with A. Grassi, J Halverson, W. Taylor, and A. Kjuchukova.
 Botong Wang:
Support of Sabbah's specialization complex
Sabbah's specialization complex is a generalization of Deligne's nearby cycles complex. We will talk about
some relations between the support of Sabbah's specialization complex, the zero locus of BernsteinSato ideal
and the cohomology support loci. This is joint work with Nero Budur, Yongqiang Liu and Luis Saumell.